Deep compartment models: A deep learning approach for the reliable prediction of time‐series data in pharmacokinetic modeling

Abstract

Nonlinear mixed effect (NLME) models are the gold standard for the analysis of patient response following drug exposure. However, these types of models are complex and time‐consuming to develop. There is great interest in the adoption of machine‐learning methods, but most implementations cannot be reliably extrapolated to treatment strategies outside of the training data. In order to solve this problem, we propose the deep compartment model (DCM), a combination of neural networks and ordinary differential equations. Using simulated datasets of different sizes, we show that our model remains accurate when training on small data sets. Furthermore, using a real‐world data set of patients with hemophilia A receiving factor VIII concentrate while undergoing surgery, we show that our model more accurately predicts a priori drug concentrations compared to a previous NLME model. In addition, we show that our model correctly describes the changing drug concentration over time. By adopting pharmacokinetic principles, the DCM allows for simulation of different treatment strategies and enables therapeutic drug monitoring.

Artificial Intelligence and Machine Learning Approaches to Facilitate Therapeutic Drug Management and Model-Informed Precision Dosing

“…Furthermore, through transfer learning, this model could predict on a small set of patient data, but there was still variability in the predictions. In addition, a study by Janssen et al 53 proposed a deep compartment model architecture that combines neural networks and ordinary differential equations to predict concentrations in simulated patients and validated it using clinical trial data. The results on simulated patients demonstrated good accuracies, with some bias in performance depending on the sampling strategy and sample size used, whereas the results using clinical trial data provided comparable accuracy to standard PK modeling.…”

Integrating machine learning with pharmacokinetic models: Benefits of scientific machine learning in adding neural networks components to existing PK models

“…Most of the existing neural network approaches do not incorporate physiological structure into the model, 13,14 however, more recently, some works have started to do this. 6,9 For example, work conducted by Qian et al 6 considers a neural network architecture which takes into consideration an ordinary differential equation (ODE) system of the PK dynamics. The work of Janssen et al 9 considers a physiologically based and well-known compartmental model for describing PK concentrations and uses a neural network term for learning covariate effects, which are incorporated as ODE parameters.…”

“…6,9 For example, work conducted by Qian et al 6 considers a neural network architecture which takes into consideration an ordinary differential equation (ODE) system of the PK dynamics. The work of Janssen et al 9 considers a physiologically based and well-known compartmental model for describing PK concentrations and uses a neural network term for learning covariate effects, which are incorporated as ODE parameters. Combining mechanistic frameworks, specifically differential equations, and ML -(called scientific machine learning [SciML]), 15,16 allows us to benefit from the advantages of both methodologies.…”

“…This work focuses on predictive models for pharmacokinetics (PKs). Most of the existing neural network approaches do not incorporate physiological structure into the model, 13,14 however, more recently, some works have started to do this 6,9 . For example, work conducted by Qian et al 6 .…”

Neural ODEs in Pharmacokinetics: Concepts and Applications

“…A main method in ML is neural networks (NNs), which is basically a non-linear function approximation approach. Due to their capability to approximate various input-output relationships, NNs were applied in different scenarios such as, (i) data imputation of missing covariates [14], (ii) covariate selection [15], and (iii) model reduction of quantitative systems pharmacology models [8]. Other publications discuss the use of NNs to approximate PK functions for concentration-time profiles and the possibility to perform PK simulations [16].…”